Some properties of $D$-weak operator topology

Year, pages: 2020, 753 - 758

Let $\mathcal{G}_D(\mathcal{H})$ denote the generalized effect algebra consisting of all positive linear operators defined on a dense linear subspace $D$ of a Hilbert space $H$. The $D$-weak operator topology (introduced by other authors) on $G_D(H)$ is investigated. The corresponding closure of the set of bounded elements of $G_D(H)$ is the whole $G_D(H)$. The closure of the set of all unbounded elements of $G_D(H)$ is also the set $G_D(H)$. If $Q$ is arbitrary unbounded element of $G_D(H)$, it determines an interval in $G_D(H)$, consisting of all operators between 0 and $Q$ (with the usual ordering of operators). If we take the set of all bounded elements of this interval, the closure of this set (in the $D$-weak operator topology) is just the original interval. Similarly, the corresponding closure of the set of all unbounded elements of the interval will again be the considered interval.

Polakovič, M. 2020. Some properties of $D$-weak operator topology. In Mathematica Slovaca, vol. 70, no.3, pp. 753-758. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0388

Polakovič, M. (2020). Some properties of $D$-weak operator topology. Mathematica Slovaca, 70(3), 753-758. 0139-9918. DOI: https://doi.org/10.1515/ms-2017-0388

Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava